publication . Doctoral thesis . 2018

Effective evolution equations from quantum mechanics

Leopold, Nikolai;
Open Access
  • Published: 28 Feb 2018
  • Publisher: Ludwig-Maximilians-Universität München
  • Country: Germany
Abstract
The goal of this thesis is to provide a mathematical rigorous derivation of the Schrödinger-Klein-Gordon equations, the Maxwell-Schrödinger equations and the defocusing cubic nonlinear Schrödinger equation in two dimensions. We study the time evolution of the Nelson model (with ultraviolet cutoff) in a limit where the number N of charged particles gets large while the coupling of each particle to the radiation field is of order N^{−1/2}. At time zero it is assumed that almost all charges are in the same one-body state (a Bose-Einstein condensate) and that the radiation field is close to a coherent state. We show the persistence of condensation over time and prov...
Subjects
free text keywords: Fakultät für Mathematik, Informatik und Statistik
Related Organizations
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue